Physics of biofilms: the initial stages of biofilm
formation and dynamics
Guillaume Lambert1, Andrew Bergman2, Qiucen Zhang3, David Bortz4 and
Robert Austin5
1
Institute of Genomics and Systems Biology, University of Chicago, Chicago, IL, USA
Physics Department, New York University, New York, NY, USA
3
Physics Department, University of Illinois, Urbana, IL, USA
4
Applied Mathematics Department, University of Colorado, Boulder, CO, USA
5
Physics Department, Princeton University, Princeton, NJ, USA
E-mail: [email protected]
2
Received 25 June 2013, revised 25 December 2013
Accepted for publication 17 February 2014
Published 8 April 2014
New Journal of Physics 16 (2014) 045005
doi:10.1088/1367-2630/16/4/045005
Abstract
One of the physiological responses of bacteria to external stress is to assemble
into a biofilm. The formation of a biofilm greatly increases a bacterial populationʼs resistance to a hostile environment by shielding cells, for example, from
antibiotics. In this paper, we describe the conditions necessary for the emergence
of biofilms in natural environments and relate them to the emergence of biofilm
formation inside microfluidic devices. We show that competing species of
Escherichia coli bacteria form biofilms to spatially segregate themselves in
response to starvation stress, and use in situ methods to characterize the physical
properties of the biofilms. Finally, we develop a microfluidic platform to study
the inter-species interactions and show how biofilm-mediated genetic interactions can improve a species’ resistance to external stress.
Keywords: microfabrication, microhabitats, aggregation, modulus, genes,
transfer, phenotype
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New Journal of Physics 16 (2014) 045005
1367-2630/14/045005+22$33.00
© 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft
New J. Phys. 16 (2014) 045005
G Lambert et al
1. Introduction
A natural response of many species of bacteria to increasing levels of stress is the formation of
biofilms, in which cells assemble together and produce large amounts of a polysaccharide-based
exopolymer matrix [1]. The biofilm developmental program usually starts with the collective
production by the cells of this dense, chemically inert exopolymer matrix as a response to
external stress (pH, osmolarity, starvation, shear) [2]. Biofilm formation is beneficial to the cell
population as a whole, since it allows cells to survive within highly stressful environments that
would prevent the survival of free-swimming cells [2]. In fact, it has been proposed that since
gene expression varies tremendously between planktonic cells and sessile cells in biofilms, they
may even be seen as two different types of differentiated cells within a multicellular organism
[3]. We will discuss this idea at the end of this paper. Figure 1 gives a very schematic picture of
the typical conception of a biofilm, although we will soon define a biofilm more generally as an
aggregate of bacteria which may or may not be fixed to a surface.
Since the diffusion of metabolites and chemicals is greatly limited inside the matrix [4], the
microenvironment created by a biofilm is highly heterogeneous and physiologically stressful
[5]. It is, however, accompanied by a high level of specialization within the bacterial
community. For example, subpopulations of bacteria inside a biofilm, each a few hundred
microns apart, may become specialized to grow aerobically, process nutrients through
fermentative pathways, digest the hydrogen sulfide produced by other cells, or resist the high
shear forces near the biofilm edge [5, 6].
In humans with bacterial infections, antibiotic treatment is often ineffective because the
limited diffusivity inside a biofilm decreases the actual dose that reaches the bacteria. This is
why biofilms are a recognized source of recurrent and persistent bacterial infections [7, 8]. As
bacteria assemble together, cell death and lysis contribute to the formation of cavities inside the
biofilm [9]. The presence of such cavities in biofilms allows cells to regain a planktonic state
and move to a different habitat [10], not unlike a metastatic expansion from a primary human
tumor.
In addition to the surface-adherent biofilms, bacteria also form aggregated communities in
suspension, which is the main subject of this article. By collision and separation, these
communities combine and recombine in a process called flocculation, and are ubiquitous from
the laboratory to the ocean [11]. These flocs are properly perceived as suspended pieces of
biofilm. Similarly to surface-adherent biofilms, the metabolic and biomechanical properties of
flocs differ greatly from those of planktonic bacteria.
Although biofilms are typically viewed in a pejorative way, they can also be extremely
beneficial. The ability of microbial communities (predominantly saprotrophic bacteria) to clean
wastewater was originally discovered by Arden and Lockett in 1913 [12] in Manchester, UK.
Primary sewage (domestic and/or industrial) was combined with flocculating micro-organisms
and aerated with the resulting mixture, reducing the organic content of the sewage. The process
was called activated sludge, in the mistaken belief that the sewage sludge had been activated,
similar to the process used to create activated charcoal6. The first large-scale activated sludge
plant was constructed in Sheffield, UK, in 1920, with widespread adoption occurring over
several years in municipalities around the globe. For more thorough and practical descriptions
6
Activated charcoal is carbon which has been processed so as to be riddled with small, low-volume pits,
increasing the surface area for adsorption or chemical reactions.
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G Lambert et al
Figure 1. Physiological representation of a biofilm. As a response to external stress
(starvation, pH, osmolarity), cells secrete an exopolymer matrix that links cells together
to form a multicellular entity called a biofilm.
of the relationship between flocculating and biofilm-forming bacterial communities and water
and wastewater treatment, we direct the interested reader to [13, 14].
Thus, biofilms are extremely important in many ways. In this article we want to examine a
more general phenomenon that can occur in almost any bacterial strain, including the ubiquitous
(in microbiology labs) strain of bacteria known as Escherichia coli. We seek to demonstrate the
generality of the initial clustering phenomena that ultimately leads to biofilm formation, as well
as the physical properties, and discuss the evolutionary (fitness) attributes that can arise when a
biofilm forms. We will discuss how microfabricated structures can be used to study the
formative dynamics of biofilms, and present some of the mysteries that arise from these devices
that we still do not understand.
2. Chemotaxis and bacterial communication
It has been shown in a beautiful set of experiments with large colonies of bacteria growing on
agar plates that bacteria can interact with each other to form complex macroscopic patterns
[15, 16]. In fact, other work has demonstrated [17, 18] that many bacteria do interact with each
other via chemical signaling when clustered together—a process called quorum sensing, driven
by a set of genes that has been well studied [19]. While there need not necessarily be a direct
signaling process between bacteria to induce efficient aggregation, recent work has shown that
bacteria actually signal each other in the initial stages of biofilm aggregation [20–22].
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G Lambert et al
To show that cell–cell communication is requited to induce cell aggregation and biofilm
formation, we first study the simplest equation that governs the physics of chemoattraction in
the absence of quorum sensing, which can be written in terms of the local densities of the
bacteria ρb and the local food density ρf as
∂ρb
= −Db 2ρb + κ ρf
dt
∂ρf
= −Df 2ρf − Cρb ρf
(1)
∂t
where Db is the effective diffusion coefficient of the bacteria at a coarse-grained level, Df is the
diffusion coefficient of nutrients, κ is the chemoattractive sensitivity and C is the consumption
rate of the food by the bacteria. In the absence of consumption or chemotaxis, the bacteria
simply diffuse with time, becoming ever more dilute. In the presence of food, the bacteria
follow food gradients. Here we make the highly simplified assumption that the coefficient of
chemoattraction κ is a constant. In addition, we assume that the food itself diffuses and is
irreversibly consumed by the bacteria.
These sets of equations have many different time-dependent solutions, which depend on
the initial conditions of the problem. The solutions do, however, have one defining
characteristic: they ultimately drive the bacteria toward dispersal, not aggregation. This can
be seen simply by noting in equation (1) that the net sign of the change in the bacterial density
with time due to food consumption is negative: as the food is consumed, the bacteria will
clearly move to regions of lower, not higher, bacterial density, to find regions where there is
more unconsumed food.
This explanation should make sense, however, bacteria donʼt necessarily disperse in this
way. Our previous results reported in [23] show that in an environment that is not boundary
free, but instead consists of many boundaries (i.e. a maze), E. coli bacteria can behave in the
opposite manner: they concentrate with time, and do not disperse, which would seem to be a
counterproductive behavior. In this paper, we explore this seemingly ‘illogical’ (i.e.
evolutionary unfit) behavior of E. coli bacteria.
The simplified set of differential equations of equation (1) fails to describe the phenomena
of cell aggregation seen when E. coli are inoculated in an environment that is bounded with a
fixed amount of food [15, 16]. The convergence of the bacteria indicates that something very
important is missing in this set of equations, namely the presence of a signaling molecule
between the bacteria that drives aggregation. Keller and Segel derived a set of differential
equations [24] that included a chemoattractant molecule that brings the bacteria together, as
opposed to the dispersal effect of pure chemotaxis in the presence of an external food source,
which is not observed in real bacterial colonies.
Cell–cell communication through a signaling field ct (x, y ) determines chemotaxis-based
bacterial movement [23] within each micro-habitat patch (MHP). Keller–Segelʼs flux [25],
which accounts for the diffusion 0 (with strength D) and the mutual chemotaxis 1 (with
strength χ),
= − D · ψt + χ · ψt · ct
(2)
0
1
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G Lambert et al
is usually used to describe the spatial dynamics ∂tψt = +
of bacterial densities ψt as a
and chemotactic spatial coupling
. At the local scale, the
function of local growth
balance between dispersive forces ( 0) and chemotaxis-based aggregation ( 1) is critically
dependent on density [26].
Let us now assume that the food used by the bacteria for metabolism has fallen to such a
low level that what remains at concentration f is being used to create a chemoattractant molecule
of concentration c, which is used to signal to the other bacteria about the forthcoming food
crisis. The Keller–Segel equations for this situation are:
∂ρ
= Db 2ρ − •[κρ c] + αρ
(3)
∂t
∂c
= Dc 2c + βfρ
(4)
∂t
∂f
= Df 2f − γρ
(5)
∂t
where γ is the rate at which the bacteria consume the food, β is the rate at which the signaling
molecule is produced by the food, κ is the chemotactic sensitivity and α is the net growth rate.
We can safely set α equal to zero here because the bacteria are presumed to be at a stationary
state due to the paucity of food.
In this case, the effect of the attractant molecule is to act between the microorganisms and
is generated by the (dwindling) food supply. Two effective ‘forces’ are at work: the dispersive
effects of diffusion (i.e. motility) and the attractive (or repulsive) response to the generated
signaling gradient. We will assume here that the sign of this latter force is attractive for the
formation of a biofilm.
We discussed in the introduction the unusual response of bacteria in a maze as the internal
medium is depleted; the bacteria cluster together into confined pockets of the maze rather than
dispersing themselves, as one would perhaps expect, in an attempt to seek out the dwindling
resources. This unusual effect of not following the food gradient can be brought out even more
starkly by microfabrication of a simple ‘castle keep’, consisting of a small square with a small
opening in it, as shown in [26]. In a normal chemotaxis experiment, bacteria might initially
enter this square, following initially higher food gradients, but would then leave the square as
this resource is exhausted. Exactly the opposite happens here: the bacteria crowd very densely
into the keep, resulting in extraordinarily high occupation densities. Such a fundamental
instability of the bacterial population can be seen in the Keller–Segel equations by a
perturbative analysis. The simplest analysis is done by setting all the time derivatives to zero in
equations (3)–(5) and setting the food concentration to some constant value of fo , to see if there
are any interesting spatial stationary states. A simple analysis reveals that the population can
sustain one-dimensional (1D) aggregates with a spatial shape given by:
ρ (x ) ∼ ρo sinh2 (x / L )
(6)
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G Lambert et al
Figure 2. The micro-habitat patch device. (a) We physically recreate a metapopulation
landscape using microfabrication. A computer-controlled microscope records the
fluorescence intensity in each chamber every 15 min.
where L is a localization length given by:
L∼
2DbDc
κρo βfo
(7)
A further instability can be discovered by analyzing how the flux of bacteria, as given by
equation (2), changes with the perturbations of bacterial density δρ in equations (3)–(4). Below
a critical concentration, perturbations lead to decreasing numbers of bacteria with time, due to
diffusion. Above a critical concentration, perturbations lead to a collapse of the bacterial
population to very high densities. The value of the critical concentration ρcrit can be found by
setting the net flux change equal to zero in the Keller–Segel equations:
δρ
δc
+ κSρcrit
0 = −DbS
(8)
lb
lc
0 = −DS
c
δc
+ Vsβfo δρ
ic
(9)
where S is the area through which the bacteria move, Vs is the enclosed volume, and lc and lb are
characteristic lengths in the evaluation of the gradients. Equations (8) and (9) then yield:
DD S
ρcrit = b c
(10)
lbβfo κ Vs
Thus, in this section, we have shown how the Keller–Segel model of bacterial selfinteractions via a signaling molecule can give rise to a fundamental instability in bacterial
populations to crowd into small volumes, which is presumably the initial stage in the formation
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G Lambert et al
Figure 3. E. coli biofilms inside micro-habitat patches (MHPs). As the density of cells
increases inside an MHP, large collections of swimming cells become sessile and
assemble into a biofilm. A few representative examples of a wild-type E. coli (a)–(c)
and wild-type (green) and GASP (red) cells (d)–(f) inside biofilms observed inside
MHPs are shown here. To guide the eye, the outline of well-defined biofilms is
highlighted in white. Note that in (a)–(c), the fluorescent signal is displayed using a
black–green–white lookup table, while the fluorescence signals in (d)–(f) are shown
using a black–green and black–red lookup table for the wild-type and GASP cells,
respectively.
of biofilms. Of course, we have not answered the deeper question of why the bacteria would
gain fitness from such a seemingly counter-productive phenotype.
3. Non-adherent biofilm formation in micro-habitat arrays
The ‘castle keep’ experiment [26] showed the fundamental clustering instability of bacterial
populations, but did not demonstrate the formation of biofilms. The traditional way to study
biofilm formation in vitro is through the use of a flow cell, a device used to culture bacteria, in
which a constant flow of nutrients induces biofilm formation through shear stress alone. The
developmental program followed by various bacterial species inside flow cells has been studied
in detail over the years, and has been very well described [27].
Biofilms, however, are present in a wide variety of natural environments, many of which
are not necessarily constantly flushed with a fluid flow of fresh nutrients. Because biofilms often
form as a response to environmental stress, we believe that the sole use of flow cells to study
biofilms fails to consider the more complex collective behaviors that are expressed by cells in
response to stress. In this section, we use an MHP system to recreate the environmental
conditions that occur in nature, and employ these conditions to induce biofilm formation in
E. coli populations.
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New J. Phys. 16 (2014) 045005
G Lambert et al
Figure 4. (a) In response to increasing cell densities, cells first form isolated biofilm
seeds, (b) which then come together to form a larger biofilm. (c) As cells pursue their
growth, the biofilm expands to fill most of the space available inside the MHP.
A micro-habitat array is a simple quasi-1D environment that generates a spatial fitness
landscape to probe the collective dynamics of cells in response to stress. A general schematic of
a micro-habitat array is shown in figure 2. The nanoslits, which connect the MHPs to the
nutrient reservoirs on either side, greatly restrict the amount of nutrients that can diffuse (not
advect) into the MHPs. These nanoslits need not be present for every MHP and can be placed as
a function of position within the array: some individual MHPs, for example, may have a full
complement of nanoslits, while others may not have any. MHPs are connected to each other via
narrow 5 μm wide channels, so cells can move between MHPs of varying food availability. As
the MHPs are not being exposed to any other regulated environment, an MHP array is most
decidedly not a chemostat, in which excess cells can flow out of the device.
Fortunately, E. coli bacteria seem to spontaneously form non-adherent biofilms inside
MHPs as the cell density increases. In fact, regardless of the fitness landscape used in our
construction of the linear array of microhabitats, we almost always observe biofilm formation
inside most MHPs. A few hours after inoculation, we typically observe cell aggregates which,
despite constant jostling by the surrounding swimming cells, maintain their shape and structure.
The fact that cells are sessile within each aggregate but are still able to resist external pressures
suggests that cohesive forces keep cells bound together. Figure 3 shows a few examples of
biofilms that are present inside MHPs for both single species (a)–(c) and competition (d)–(f)
experiments. We will discuss these different kinds of experiments in section 4. To guide the
eye, we have added a white outline around the well-defined biofilms, which we could make out
as a result of their collective motion.
Note that the morphology of each biofilm is very irregular, meaning that biofilm growth is
probably not occurring isotropically. In addition, the shape of different biofilms grown under
the same experimental conditions varies tremendously, with structures ranging from simple
microcolonies to multiple colonies linked to one another by dendrite-like protrusions. Several
studies have used 3D reconstructions from confocal imaging to quantify the physical parameters
of biofilms, such as the surface-to-volume ratios and, perhaps out of mathematical hubris,
fractal dimensionality [28, 29].
The type of biological (as opposed to physical) stress that is pushing cells to assemble
together and form biofilms inside MHPs remains unknown; we have not yet developed a
reliable way to monitor the gene expression of the metabolic state of these bacteria in situ.
Future experiments could improve upon this weakness of these experiments by extracting cells
from the MHPs for gene expression analysis or, alternatively, using fluorescent reporters tied
to the expression of known stress response genes to directly monitor their levels of expression.
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G Lambert et al
A few clues, however, seem to indicate that an increased cell density plays an important role in
biofilm genesis.
Figure 4 shows the development of a single-species biofilm inside an MHP. First, cells
form small aggregates inside the MHPs. Then, as the density of the cell increases, the biofilm
aggregates assemble together and progressively expand to occupy most of the space available.
The propensity of wild-type cells to form biofilms strongly depends on the nutrient levels; we
observe that in an alternating nutrient landscape, biofilms mainly form in the nutrient rich (NR)
regions [30]. Since starvation occurs in NP regions first, this seems to indicate that biofilm
formation is not tied to a lack of nutrients but to the increase in cell density.
Obviously, there is a collective nature to these biofilms’ development. This collective
nature makes sense in light of what we discussed above when we considered the Keller–Segel
equations (equations (3)–(5)), namely that bacterial behaviors are directly related to cell
densities and cell–cell communication. We should also associate this collective nature with the
phenomena of quorum sensing—a process through which certain genes or behaviors are only
expressed in response to a sufficiently high cell density [31]. In fact, E. coli has the ability to
form biofilms in response not only to stress [32, 33], but also to an increase in cell density alone
through quorum sensing [34], although we suspect the two phenomena are highly inter-related.
In the case of mutant cells displaying a growth advantage in the stationary phase (GASP)
phenotype, we expect their development to be different from that of wild-type cells. GASP
mutants are adapted to grow in stressful environments and can diversify their nutrient sources to
reach a final density inside MHPs that is higher than that of wild-type cells. The development of
the biofilm remains fairly similar to that of wild-type cells and, as such, we do not deem it
necessary to illustrate it. A major difference, however, is that biofilms comprised of GASP
mutants reach much higher densities that those comprised of wild-type cells [30]; indeed, while
wild-type cells form biofilms in less than 30% of the NP MHPs, GASP cells appear to form
biofilms in 100% of these NP MHPs. This observation, considered in light of the fact that
GASP mutants maintain a proliferative phenotype despite deteriorating growth conditions, is
consistent with our proposition that biofilm formation is a direct consequence of high cell
densities.
4. Biofilm development under competition
Previous studies have shown that under prolonged growth in the absence of agitation, GASP
and wild-type strains of E. coli are both able to form biofilms [35]. Given what we have shown
in the previous section, that biofilm development for E. coli is highly dependent on the
planktonic cell density, one might therefore expect that the more complex redistribution of cells
found during competition experiments, especially those observed in rapidly alternating fitness
landscapes, would translate into more complex biofilm developmental dynamics. In particular,
the relative fraction of each cell type in the NR and NP MHPs may translate into very different
accretion dynamics in each habitat. In order to study these accretion dynamics, we analyze
biofilm development on the microscopic scale—i.e. in single MHPs.
The steps involved in the biofilmʼs developmental progression in our device [30] are
shown in figure 5(a)–(d). In order to delineate different phenotypes of the cells, we use wildtype cells that express green fluorescent proteins (GFP-WT) and GASP mutants that express red
fluorescent proteins (RFP-GASP). As a function of time after inoculation of the MHPs, first,
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New J. Phys. 16 (2014) 045005
G Lambert et al
Figure 5. Biofilm development under competition. Since GASP cells fail to enter a
stationary phase, (a) after the biofilm seeds form and (b) assemble together, they readily
(c) outcompete the wild-type cells and contribute to most of the biofilm growth. (d) As
growth occurs in the NR MHP, high cell density quenches the population distribution.
small aggregates of GFP-WT cells form inside the NR regions and assemble together
(T = 16 h ). RFP-GASP cells then join the wild-type aggregate and expand around it
(T = 18 h ). RFP-GASP cells near the edge of the biofilm proliferate to fill most of the NR
habitat (T = 20 h ), which in turn gradually limits the space available for free-swimming
bacteria in the NR MHPs. As a result, RFP-GASP cells in the biofilm progressively become the
dominant strain in the NR regions.
GFP-WT cells, on the other hand, are still in a planktonic state in the NR regions. As the
biofilm expands, the space available in the NR regions decreases and GFP-WT cells diffusively
migrate into the NP regions. The increasing GFP-WT cell density in the NP regions also favors
the formation of small cell aggregates (T = 20 h), which eventually fill all the space available in
the NP MHPs, as swimming cells continue to migrate into them. After T = 36 h, there is no
‘free’ space available in either type of habitat, as most MHPs are packed with biofilms. The
population distribution is thereby locked and no more inter-MHP cell exchange is possible,
leaving a large frequency of RFP-GASP cells in the NR MHPs and GFP-WT cells in the NP
MHPs.
5. Physical properties of non-adherent biofilms
The phenomenological description of a biofilm's development, although illustrative, remains
mainly qualitative. As shown above, cells growing on their own or under competition
conditions have slightly different developmental programs. The presence of two species with
different growth phenotypes influences the overall spatial distribution, and cellular segregation
by phenotype occurs locally. In fact, similar spatial arrangements have been demonstrated in
dental biofilms (commonly known as dental plaque); cells from totally different species, most of
them unculturable outside of a dental plaque environment, spatially distribute themselves into
highly organized layers [36].
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New J. Phys. 16 (2014) 045005
G Lambert et al
Figure 6. Cells embedded into biofilms. We visualize the microstructure of biofilm
aggregates by inoculating our device with 1% RFP-producing cells. As cells randomly
embed themselves into biofilm structures, we use these RFP-producing cells to extract
the microscopic properties of the biofilms.
In this section, we use more quantitative tools to describe the physical properties of the
biofilm aggregates we observe inside our MHP devices. For the sake of simplicity, we only
study the emergent physical properties of wild-type biofilms. In particular, we study the overall
motion of biofilm aggregates inside a densely populated bath of swimming cells. We then
describe how the constant external pressure exterted by the planktonic cell population deforms
these biofilms, and we link these deformations with density variations of the bacterial quasifluid. As the biofilm increases in size, we show that cells gradually embed themselves into the
ever-growing biofilm.
Before diving into the results and the detailed analysis performed for this section, we first
digress to describe the technique used to extract the physical properties of the studied biofilms.
As shown in figure 3, biofilms inside MHPs are heterogeneous and display a wide variety of
different structures. Furthermore, the inherently high density of cells reached inside biofilms,
coupled with the limited numerical aperture of our microscopy setup, renders the localization of
single cells challenging.
The localization and tracking of single cells at low densities, however, is relatively simple.
We therefore combine low-density tracking to high-density biofilm monitoring by seeding
MHP devices with RFP- and GFP-producing wild-type cells (GFP-WT and RFP-WT,
respectively) at relative initial densities of 1–100. As a result, we can track the qualitative
biofilm development by monitoring the GFP fluorescence of an MHP, and we can extract the
localization of single cells inside a biofilm by recording the RFP fluorescence. Figure 6 shows a
composite micrograph of a GFP-WT biofilm, of which 1% of the cells are RFP-WT: in this
particular example, four RFP-WT cells are embedded in a GFP-WT biofilm aggregate. We can
extract the position of each embedded RFP-WT cell and then use their position to extract the
overall biofilm motion and the amount of strain the aggregate is subjected to.
The physical properties of these non-adherent biofilms are interesting: their deformation
can be measured as a function of time, as they are subjected to physical forces due to the
external impulses supplied by collisions with surrounding planktonic cells. Biofilms are usually
cultured on glass slides under a constant fluid flow, and their elastic properties can thus be
thoroughly studied by modulating the flow rate and studying their deformation [37]. Results
seem to indicate that biofilms behave as viscoelastic fluids under these conditions, and that they
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New J. Phys. 16 (2014) 045005
G Lambert et al
Figure 7. Strain inside a biofilm. In this example, the area enclosed by seven embedded
RFP-WT cells is monitored over time. The temporal variations in the area defined by
these cells varies by 15% (rms measurements).
typically have relatively long relaxation times of approximately 18 min [38] in response to
mechanical stress. Here, we want to test whether the same physics also occurs for biofilms
inside MHPs, despite different growth conditions. In particular, biofilms in MHPs are grown
without shear stress and, in addition, form at length scales somewhat smaller than those usually
observed in flow chambers: about 50–75 μm in linear length inside MHPs, as compared with
150–200 μm.
We may associate the random collisions between swimming cells and the biofilm with
random collisions between water molecules and a sphere. A caveat here is that the temperature
does not affect the motion of cells the same way that it affects the motion of water molecules;
since temperature provides kinetic energy to a molecule, the analog of the ‘temperature’ of a
bacterial bath is related to the swimming velocity of each cell. Luckily, E. coli swimming velocity
remains constant over a wide range of environmental conditions at about 25 μm s−1 [39].
Experiments with small ‘inactive’ objects—for example, polystyrene beads less than
10 μm in diameter—show that diffusion inside a bacterial bath is very similar to Brownian
motion [40]. Associating an effective temperature T to the diffusion constant D for beads of
radius r inside a bacterial bath with fluid viscosity η, we use the Stokes–Einstein relation:
kT
D= B
(11)
6πηr
This leads to an effective temperature ‘TBact ’ which is 100 times higher than room
temperature. We will refer to the effective temperature as TBact ≡ 100 × TRoom and will use this
important result to compute the Youngʼs modulus and rigidity modulus of biofilm aggregates.
The random collisions of swimming bacteria surrounding the biofilms thus act as a bath
that applies force to the biofilms. In fact, these forces induce significant strain on the biofilm,
which we will quantify in light of the random density fluctuations inside the surrounding
bacterial bath. To measure the strain of a biofilm, we use datasets in which five to seven red
fluorescent protein-expressing wild-type cells (RFP-WT) are embedded, purely by chance, into
a single biofilm aggregate, as shown in figure 7. Having more than three embedded cells greatly
increases the amount of information that can be extracted, because the biofilm deformation can
be determined at a higher precision.
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We first plot the relative change in the total area delimited by the embedded RFP-WT cells
inside the biofilm aggregate, seen as the enclosed region in figure 7. A computed algorithm
generates the outline of the area enclosed by the cells and we monitor the root–mean squared
variations over time to find that, surprisingly, the variations in the total area are approximately
15% (rms measurement), but can have peaks as large as 20%—which is substantial considering
that they are mainly due to in situ pressure variations caused by swimming cells. Considered in
terms of the viscoelastic properties of a biofilm, these results would suggest that the biofilmʼs
bulk modulus B:
∂P
B = −V
(12)
∂V
is quite small relative to many other materials, where v is the volume of the aggregate and p is
the external pressure on the aggregate.
We estimate the magnitude of the bulk modulus from simple thermodynamic arguments.
In an MHP, variations in biofilm volume result from fluctuations in the effective external
pressure exerted on the biofilm aggregate by the surrounding motile bacteria. Since external
collisions with swimming cells, not flow perturbations caused by swimming cells, are the main
contributor of pressure against the biofilms [41], we associate these pressure fluctuations with
local fluctuations in the number of cells in the bacterial bath. Simha and Ramaswamy have
in a suspension of self-propelled particles scales as
shown that the relative number variation δN
N
N 2/3 [42]. Accordingly, relative differences in pressure also scale as
δN
N 2/3
, assuming that an ‘ideal
gas’-like expression such as pV ∼ NkBTBact holds for bacterial baths, which is a reasonable
approximation considering the fact that Wu et al demonstrated that the velocity distribution of
bacteria at high densities is similar to that of an ideal gas [40].
In particular, assuming that the observed changes in volume of the biofilm are negligible as
compared with the MHP volume, we can use the estimated density of motile bacteria and the
expression for pressure fluctuations δP given by δP ∼ ρkBTBact δNN for a cell density ρ inside the
MHPs. From our previous estimate that the cell density is approximately 3 × 105 cells per MHP
[43], we obtain a pressure variation δP ∼ 10 2 Pa.
To estimate the bulk modulus of the biofilm, we discretize B as δAδP/ A and use the biofilmʼs
root–mean squared volume variation, measured in figure 7, of 15% to find that B ∼ 600 Pa.
This derivation is not meant to be taken as an absolute determination of the bulk modulus of a
biofilm aggregate, but rather as a back-of-the-envelope estimate. This value is not, however, too
far from the values observed in flow chamber work, which range from 17 to 300 Pa [37]. We
compare this Youngʼs modulus with other biological materials in table 1. Our approximation of
the Youngʼs modulus of a biofilm is in good agreement with other reported values [37, 44].
6. Biofilms as clonal communities
Biofilms generally grow on surfaces and, following a period of attachment, cells within the
biofilm form microcolonies that protrude away from the attachment plane. The microcolonies
grow away from surfaces to distance themselves from competing cells and gain better access
to nutrients in a manner analogous to tree growth in a forest: as plants compete for the
same resource (light), the only way to outcompete their neighbors is to grow higher and wider.
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Table 1. The modulus of elasticity in pascals (Pa) associated with different biological
structures.
Material
Modulus (Pa)
Biofilm (volume fluctuations, here)
600
Biofilm (flow chambers [37])
17–240
Biofilm (point of failure measurements [44]) 6500
Brain tissue [45]
4 × 104
Muscle tissue [46]
10 5
Bone [47]
3 × 1010
Tooth enamel [48]
1011
As a result, the structure of biofilms is inherently three-dimensional. The biofilm representations
and analyses presented up until now have failed to emphasize this point.
Confocal imaging is a microscopy technique that achieves spatial resolutions and contrast
levels much higher than are possible with regular epifluorescence microscopy. By rejecting
most of the out-of-plane light using a pinhole in the conjugate plane of the detector, it is
possible to reconstruct 3D volumes by recording planar sections of a material. Ever since the
first 3D reconstruction of a biofilm using confocal imaging was published in 1991 [49],
confocal imaging has been widely used as a non-destructive tool to study the microscopic
properties of biofilms in situ. In this section, we use scanning laser confocal microscopy to
study the developmental dynamics and the collective behaviors of E. coli bacteria inside MHPs.
We aim to determine whether we can extract the developmental dynamics of biofilm
formation from a 3D reconstruction made using confocal imaging. In particular, we inoculate an
MHP device with a 1:1 ratio of GFP-WT and RFP-WT cells, and culture them for 24 hours to
allow for sufficient growth and biofilm formation. The fact that cells of each phenotype are
present in a 1:1 ratio helps to better capture large-scale structures within the biofilm, as
compared with the 1% inoculation experiments. We first record and construct a 3D
representation of a biofilm, as shown in figure 8, and compare the structures produced by
the cells in the two different color channels. Using this representation, we can locate range
expansions of individual genotypes simply by observing whether or not large monochromatic
domains are present in the biofilm.
The structure of the biofilm shown in figure 8 is extremely rugged, although there are
domains of predominantly green (or red) cells, as indicated by the arrows in figure 8.
Furthermore, many of these domains are connected; a large fraction of the cells inside the
biofilm are actually part of the ‘same’ biofilm formation. These domains are only 5–10 μm wide
and their presence suggests that clonal growth (i.e. growth from a single founder population) is
occurring within this particular biofilm.
The situation presented here is similar to the one presented in work done by Hallatschek
et al, in which they study genetic drift and gene segregation in growing colonies of bacteria
[50]. They showed that in the absence of genetic selection, a gene may still fix in a population
due to genetic drift alone. We next attempt to better characterize the structure of biofilms inside
MHPs to capture the truly three-dimensional nature of biofilms. In particular, we use intensity
correlations to determine whether growth within a biofilm leads to clonal expansion due to
genetic drift, a phenomenon already observed and characterized in bacterial colonies growing
on agar plates [50].
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G Lambert et al
Figure 8. Three-dimensional reconstruction of a biofilm. The 3D structural information
of a biofilm can be extracted from confocal imaging of two wild-type populations (GFPWT and RFP-WT) growing inside an MHP.
Figure 9. Spatial correlations. We measure the spatial autocorrelation (circles) and
cross-correlation (squares) between the two species. Note that the cross-correlation is
decreasing at small distances, an indication of some kind of hard-core repulsion
between each cell. In the inset, we measure how the autocorrelation and crosscorrelation distances vary with depth.
We first characterize the spatial correlations within and between each species in figure 9.
Specifically, we compute cauto (r ), the correlation of a single genotypeʼs density to all points
located a radial distance r away, using cauto = ρi (x ⃗ ) ρi (x ⃗ + r ) , where ρi (x ⃗ ) is the fluorescence
intensity of species i at location x ⃗ and the brackets denote an average over all points x ⃗ .
Similarly, we measure ccross (r ), the cross-correlation between the GFP-WT and RFP-WT
populations using ccross = ρi (x ⃗ ) ρj (x ⃗ + r ) . Figure 9 shows the functional dependence of
cauto (r ) and ccross (r ) (circles and squares, respectively) at a depth z = 7 μm . Note that
autocorrelation decays exponentially with increasing r, thereby providing a characteristic length
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G Lambert et al
Figure 10. Vertical cell distribution. A representative example of a section of a biofilm
shows vertically aligned domains of segregated GFP-WT or RFP-WT cells. The image
is treated with an intensity threshold to better illustrate cell segregation.
scale of a single-species biofilm. The cross-correlation ccross (r ), on the other hand, progressively
increases with r due to the volume exclusion between the two species. The characteristic length
scale of this increase will also provide an indication of the characteristic aggregate size of the
biofilm.
We extract characteristic length scales for the autocorrelation and cross-correlation to be
approximately 3.5 and 2.5 μm, respectively, by fitting an exponential function to the measured
correlations (figure 9, inset). Note that while there is an inherent exclusion between the GFPWT and RFP-WT, which is simply due to the size of each cell, these length scales are somewhat
greater than a single cell, which is usually ∼0.5 μm wide and ∼2 μm long. These results indicate
that cell aggregation is occurring at scales many times larger than a single cell. The size of the
clonal expansion inside MHPs, however, is much smaller than that of colonies grown on agar
plates [50], which eventually grow to be millimeter-sized.
We then characterize the genetic correlation of a biofilm along the z-direction by using the
information about the depth-dependent cell distribution obtained from the confocal
reconstruction. In figure 10, we show the fluorescence intensities as a vertical cross-section
of the biofilm presented in figure 8. Note the presence of vertical domains of predominantly
GFP-WT or RFP-WT cells. We create a binary image of the cross-section (using an intensity
threshold of 75% of the maximum intensity) to better visualize the domains. Interestingly, the
amount of overlap between the two genotypes is very small (these appear as yellow regions in
the lower panel of figure 10) and the extent of the vertical domains is almost as high as the
device itself.
The observations in figure 10 confirm a few assumptions. First, biofilm growth does seem
to occur through genetic expansion, which is confirmed by the fact that we observe ‘vertical’
domains having the same phenotype in the 1:1 GFP-WT:RFP-WT biofilms. If the primary
cause of growth were the random attachment of cells to the surface of the biofilm aggregate, we
would not observe these domains. Second, biofilms do, in fact, seem to be attached to the floor
of the MHPs when they are growing. This is indicated by the fact that these biofilms form
vertical domains, meaning they probably grow upwards (toward the top of the MHP, where
there is presumably less competition) from their attachment planes.
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G Lambert et al
7. Conclusions and future directions
We have shown how we can use microfluidic technologies to study the development and
evolution of biofilms. First we showed that the Keller–Segel model, when applied to bacterial
self-interactions via signaling molecules, provides the first step toward the formation of biofilms
through a fundamental instability, which prompts bacterial populations to crowd into small
volumes. Then we described the developmental steps followed by a single species of bacteria as
it forms biofilms inside micro-habitats with limited nutrient access. We next investigated the
influence of biofilm formation on the competition dynamics of two bacterial species, and
showed that each species spatially segregate themselves into habitats having access to different
levels of nutrients. We continued to study the physical properties of non-adherent biofilms to
measure their viscoelastic properties, and then used confocal microscopy to characterize the
spatial distribution of cells within a biofilm to find that biofilm growth occurs through clonal
expansion at the surface of the biofilms. We finished by describing a model system that allows
us to study horizontal gene transfer (HGT) between spatially isolated biofilm populations.
Using our model system, we described interesting events that seem to suggest that HGT,
conferring antibiotic resistance, occurs between weakly interacting bacterial populations.
The remainder of this section will be rather speculative, and linked to the observation that
the bacteria, which show quite different behavior at high cell density than free-swimming
bacteria, are spending a significant fraction of their lifetime in a sessile state within the biofilms.
In particular, we are interested in understanding the role that biofilm micro-habitats have in the
evolution of bacterial communities. Indeed, it has been shown that the proximity of cells within
a biofilm increases the potential for genetic exchange between individuals [51–53]. This genetic
exchange often occurs through HGT, a general term for the transfer of genetic material between
two organisms that may or may not be a member of the same species. HGT occurs in contrast to
the transfer of genetic material from parent to offspring—called vertical gene transfer, or, more
commonly, reproduction—that gave rise to the classic concept of Darwinian evolution. HGT
occurs in nature through a number of different mechanisms, such as transformation, viral
transduction and bacterial conjugation, and can result in either permanent genetic changes, if
DNA is recombined into an organismʼs genome, or temporary changes, if organisms take up
DNA but do not incorporate it into their genome.
As discussed above, E. coli have the ability to form biofilms, not only in response to stress,
but also as a result of quorum sensing or as a response to an increase in bacterial density
[30, 34]. A study by Maeda et al showed that when two different E. coli strains containing
plasmids that confer different antibiotic resistances were allowed to form biofilms on pieces of
membrane filter, some members of the population would undergo transformation to become
doubly resistant [52]. Maeda et al measured that this would occur at a low frequency of between
10−10 and 10−9 per recipient cell [52]. Another study by Sun et al used stationary E. coli cultures
to form biofilms and measured a transformation frequency of 10−6 to 10−5, which they noted is
higher than the efficiency of some naturally competent bacteria, like M. smegmatis [54].
Though more work certainly needs to be done to fully characterize the behavior of E. coli
within biofilms, we can understand from these studies that genetic exchange between bacteria
not typically thought of as ‘naturally competent’ is certainly possible, and is spurred on greatly
under conditions of stress and the formation of biofilms.
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New J. Phys. 16 (2014) 045005
G Lambert et al
Figure 11. (a) Schematic of the double 1D MHP chip used in the E. coli transformation
experiments, showing MHPs in red, reservoirs in green and nanoslits as groups of
dashes. (b) Scanning electron micropsope image of one of the double 1D MHP devices
used in the proposed transformation experiments. Upon lysis, a cell releases its
plasmids, which can then move across the nanoslits and be taken up by the cell in the
other population. (c) Images of the same group of MHPs over a period of about 12 h,
produced from merging the green and red channels. The production of RFP in the row
to the right, which was only inoculated with GFP-producing bacteria, indicates the
emergence of a doubly resistant population.
Our goal here is to study the capture of free DNA by competent E. coli cells. The general
idea behind our experiment is to inoculate a device with two different strains that are able to
interact and share media, but do not share physical space. To achieve this, we use two different
strains of antibiotic-resistant E. coli, with different fluorescent markers on their respective
plasmids, and observe the uptake by each strain of the other strainʼs plasmid as it is released into
the environment. To ensure that DNA transfer does not occur through physical contact between
individuals, we keep each population physically separated, so that they can not intermingle and
form heterogeneous biofilms, in which we might not be able to make out the few cases of
transformation.
The new device was obtained through a simple modification to the device described in the
previous sections. Instead of one row, the new device has two rows of MHPs, in which the
adjacent, interacting populations can grow and exchange genetic material through the 100 nm
deep nanoslits (figure 11(a)). We use a separate inoculation port for each row, one on either end
of the device, to ensure no cross-contamination occurs between each row of MHPs following
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New J. Phys. 16 (2014) 045005
G Lambert et al
Figure 12. Cell–cell interactions. No tumor cell is acting alone. Strong interactions
among different cell types (tumor cells, fibroblasts, endothelial cells) often give rise to
an increased adaptability and more complex behaviors.
the initial cell inoculation. Though the nanoslits restrict the bacteria themselves from moving
between the two rows, they do still provide for the free exchange of media, including plasmids
that might be present in that media. So, if a cell containing plasmids were to lyse, releasing its
contents into the media, those plasmids would then be free to diffuse across the nanoslits and be
taken up by cells on the other side. A cartoon depiction of this process is shown in figure 11(b).
To observe the transformation occurring between two bacterial populations, we inoculated
one row with GFP-producing, ampicillin-resistant E. coli and the other with RFP-producing,
kanamycin-resistant E. coli. By flowing media containing each antibiotic in the reservoir closer
to the strain with resistance to that antibiotic, as shown in panel (1) in figure 11(c), we produced
a concentration gradient of each antibiotic across the width of the device. On both sides, the
stronger concentration of antibiotic from the closer reservoir did not greatly affect the
population with resistance to that antibiotic, but the weaker concentration from the further
reservoir did produce a significant stress on the bacteria. This stress, felt by both populations,
increases the competency rate of cells [54] and makes uptake of the plasmid from the other
population favorable.
In figure 11(c), we observe a transfer of antibiotic resistance between the two isolated
populations, but only between MHPs in which there was high cell density and significant
biofilm development. In panel (1), the biofilms have already formed, though the cluster of RFPproducing, kanamycin-resistant bacteria in the bottom MHP have already begun to reduce in
cell density. After a few hours, once many of these bacteria have died and released their
plasmids into the media, a small population of bacteria begins to grow in the void left by the
GFP-producing bacteria. This growth is newly visible in panel (2). For a couple of hours this
new population appears to be producing only GFP, but it soon begins producing significant
levels of RFP as well, indicating an event where transmission of antibiotic resistance between
the two populations has occurred.
It is exciting to observe this kind of rapid migration of cells between MHPs following the
exchange of a plasmid between two physically separated biofilms in a stressed environment.
The close correlation of these two events indicates that this type of design could very rapidly
select cells that have acquired resistance through HGT.
On a more speculative note, we have recently proposed that the physical properties of
biofilms, as well as their developmental progression, mirror the destructive growth of cancer
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G Lambert et al
tissues within a host [55]. In biofilm communities, cells may switch metabolic states to cope
with the limited influx of nutrients and oxygen due to the decreased diffusion of chemicals
through the biofilm matrix. A similar cell specialization is also observed in cancer tissues: in
addition to proliferative cancer cells, a tumor is also composed of specialized cells (e.g.
fibroblasts, immune cells and endothelial cells, as shown in figure 12) that contain genetic
alterations and actually co-evolve with the cancer cells [56, 57]. For instance, an extracellular
matrix is produced in anomalously high quantities in tumors by stromal cells [58] and, like
bacterial biofilms, limits the ability of chemotherapeutic drugs to penetrate the tumor. Since the
additional matrix deposition also limits the diffusion of oxygen and nutrients into the tumor
tissue, tumor cells switch to a fermentative metabolism (glycolysis) that consumes glucose
without oxygen. Aerobic glycolysis of the cancer cells releases lactose, which contributes to the
acidification of the tumor microenvironment [59]. It has been shown that surrounding
fibroblasts and endothelial cells cope with this harmful environment by increasing the rate of
lactate metabolism to lower the pH of the environment [60].
Cancer tissues are thus a sophisticated collection of specialized cells that co-evolve with
tumor cells to sustain the high metabolic needs of the tumor cells. This adaptation leads to levels
of specialization by different cell types that go beyond the naive view that cancer tissues are
highly disorganized. Although some levels of disorder are present within cancer tissues, the
levels of specialization of the epithelial/stromal cell collective is in some ways very similar to
the spatial variation and adaptation observed in biofilm communities. A better understanding of
the complex symbiotic interplay between different cells within a bacterial biofilm may facilitate
the study of analogous development within cancer tissues.
Acknowledgments
This work was performed in part at the Cornell NanoScale Facility, a member of the National
Nanotechnology Infrastructure Network, which is supported by the National Science
Foundation (grant no. ECS 03-35765). The research described was supported by an award
(U54CA143803) from the US National Cancer Institute and in part by the National Science
Foundation under grant no. PHYS-1066293, and the hospitality of the Aspen Center for
Physics. DB thanks the NSF for NSF PHY-0940991. The content is solely the responsibility of
the authors and does not necessarily represent the official views of the National Cancer Institute,
the National Institutes of Health or the National Science Foundation.
References
Branda S S, Vik A, Friedman L and Kolter R 2005 Trends Microbiol. 13 20–26
Monds R D and O’Toole G A 2009 Trends Microbiol. 17 73–87
Stoodley P, Sauer K, Davies D G and Costerton J W 2002 Annu. Rev. Microbiol. 56 187–209
Stewart P S 2003 J. Bacteriol. 185 1485–91
Stewart P S and Franklin M J 2008 Nature Rev. Microbiol. 6 199–210
Rani S A, Pitts B, Beyenal H, Veluchamy R A, Lewandowski Z, Davison W M, Buckingham-Meyer K and
Stewart P S 2007 J. Bacteriol. 189 4223–33
[7] Costerton J W, Stewart P S and Greenberg E P 1999 Science 284 1318–22
[8] Donlan R M and Costerton J W 2002 Clin. Microbiol. Rev. 15 167–93
[1]
[2]
[3]
[4]
[5]
[6]
20
New J. Phys. 16 (2014) 045005
G Lambert et al
[9] Ma L, Conover M, Lu H, Parsek M R, Bayles K and Wozniak D J 2009 PLoS Pathog. 5 e1000354
[10] Stoodley P, Wilson S, Hall-Stoodley L, Boyle J D, Lappin-Scott H M and Costerton J W 2001 Appl. Environ.
Microbiol. 67 5608–13
[11] Liss S N, Droppo I G, Leppard G G and Milligan T G (ed) 2004 Flocculation in Natural and Engineered
Environmental Systems 1st edn (Boca Raton, FL: CRC Press)
[12] Ardern E and Lockett W T 1914 Journal of the Society of Chemical Industry 33 523–39
[13] Bache D M and Gregory R 2007 Flocs in Water Treatment (London: IWA Publishing)
[14] Wuertz S, Wilderer P A and Bishop P L (ed) 2004 Biofilms in Wastewater Treatment: an Interdisciplinary
Approach 1st edn (London: IWA Publishing) ISBN 1843390078
[15] Budrene E O and Berg H C 1991 Nature 349 630–3
[16] Budrene E O and Berg H C 1995 Nature 376 49–53
[17] Waters C M and Bassler B L 2005 Annu. Rev. Cell Dev. Biol. 21 319–46
[18] Camilli A and Bassler B L 2006 Science 311 1113–6
[19] Schauder S, Shokat K, Surette M G and Bassler B L 2001 Mol. Microbiol. 41 463–76
[20] Defoirdt T 2011 ISME J. 5 569–70
[21] Hegde M, Englert D L, Schrock S, Cohn W B, Vogt C, Wood T K, Manson M D and Jayaraman A 2011
J. Bacteriol. 193 768–73
[22] Wu H C et al 2013 Mol. Syst. Biol. 9 636
[23] Park S, Wolanin P M, Yuzbashyan E A, Silberzan P, Stock J B and Austin R H 2003 Science 301 188
[24] Keller E F and Segel L A 1971 Mol. Syst. Biol. 30 235–48
[25] Keller E F and Segel L A 1970 Mol. Syst. Biol. 26 399–415
[26] Park S, Wolanin P M, Yuzbashyan E A, Lin H, Darnton N C, Stock J B, Silberzan P and Austin R 2003 Proc.
Natl Acad. Sci. USA 100 13910–5
[27] O’Toole G, Kaplan H B and Kolter R 2000 Annu. Rev. Microbiol. 54 49–79
[28] Yang X, Beyenal H, Harkin G and Lewandowski Z 2000 J. Microbiol. Methods 39 109–19
[29] Heydorn A, Nielsen A T, Hentzer M, Sternberg C, Givskov M, Ersbll B K and Molin S 2000 Microbiology
146 2395–407
[30] Lambert G, Liao D, Vyawahare S and Austin R H 2011 J. Bacteriol. 193 1878–83
[31] Miller M B and Bassler B L 2001 Annu. Rev. Microbiol. 55 165–99
[32] Hall-Stoodley L, Costerton J W and Stoodley P 2004 Nature Rev. Microbiol. 2 95–108
[33] Davey M E and O’Toole G A 2000 Microbiol. Mol. Biol. Rev. 64 847–67
[34] Gonzlez Barrios A F, Zuo R, Hashimoto Y, Yang L, Bentley W E and Wood T K 2006 J. Bacteriol. 188
305–16
[35] Kraigsley A M and Finkel S E 2009 FEMS Microbiol. Ecol. 293 135–40
[36] Marsh P D 2005 J. Clin. Periodontol. 32 Suppl 6 7–15
[37] Stoodley P, Lewandowski Z, Boyle J D and Lappin-Scott H M 1999 Biotechnol. Bioeng. 65 83–92
[38] Shaw T, Winston M, Rupp C J, Klapper I and Stoodley P 2004 Phys. Rev. Lett. 93 098102
[39] Maeda K, Imae Y, Shioi J I and Oosawa F 1976 J. Bacteriol. 127 1039–46
[40] Wu X L and Libchaber A 2000 Phys. Rev. Lett. 84 3017–20
[41] Drescher K, Dunkel J, Cisneros L H, Ganguly S and Goldstein R E 2011 Proc. Natl Acad. Sci. 108 10940–5
[42] Aditi Simha R and Ramaswamy S 2002 Phys. Rev. Lett. 89 058101
[43] Lambert G 2011 Emergent collective behavior of microorganisms PhD Thesis Department of Physics,
Princeton University, Princeton, New Jersey
[44] Korstgens V, Flemming H C, Wingender J and Borchard W 2001 J. Microbiol. Methods 46 9–17
[45] Hirakawa K, Hashizume K and Hayashi T 1981 Brain and Nerve 33 1057–65
[46] Lieber R L 2009 Skeletal Muscle Structure, Function, and Plasticity 3rd edn (Philadelphia, PA: Lippincott
Williams & Wilkins)
[47] Spatz H C, O’Leary E J and Vincent J F 1996 Proc. Roy. Soc. B Biol. Sci. 263 287–94
[48] Mahoney E, Holt A, Swain M and Kilpatrick N 2000 J. Dent. 28 589–94
21
New J. Phys. 16 (2014) 045005
[49]
[50]
[51]
[52]
[53]
[54]
[55]
[56]
[57]
[58]
[59]
[60]
G Lambert et al
Lawrence J R, Korber D R, Hoyle B D, Costerton J W and Caldwell D E 1991 J. Bacteriol. 173 6558–67
Hallatschek O, Hersen P, Ramanathan S and Nelson D R 2007 Proc. Natl Acad. Sci. 104 19926–30
Sorensen S J, Bailey M, Hansen L H, Kroer N and Wuertz S 2005 Nature Rev. Microbiol. 3 700–10
Maeda S, Ito M, Ando T, Ishimoto Y, Fujisawa Y, Takahashi H, Matsuda A, Sawamura A and Kato S 2006
FEMS Microbiol. Lett. 255 115–20
Madsen J S, Burmolle M, Hansen L H and Sorensen S J 2012 FEMS Immunol. Med. Mic. 65 183–95
Sun D, Zhang Y, Mei Y, Jiang H, Xie Z, Liu H, Chen X and Shen P 2006 FEMS Microbiol. Lett. 265 249–55
Lambert G, Estvez-Salmeron L, Oh S, Liao D, Emerson B M, Tlsty T D and Austin R H 2011 Nature Rev.
Cancer 11 375–82
Liotta L A and Kohn E C 2001 Nature 411 375–9
Joyce J A and Pollard J W 2009 Nature Rev. Cancer 9 239–52
Kalluri R and Zeisberg M 2006 Nature Rev. Cancer 6 392–401
Gatenby R A and Gillies R J 2004 Nature Rev. Cancer 4 891–9
Koukourakis M I, Giatromanolaki A, Harris A L and Sivridis E 2006 Cancer Res. 66 632–7
22